I have searched the Pokemon website and I found not trainer, Pokemon, or energy card that could yield a clue for a core. My best guess that a core in the TCG is either is similar to in the actual games/showdown or simply nonexistent in the realm of Pokemon TCG. I could have missed some card that indicates what your looking for, but is unlikely.

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Oh, Cores are the thing that decks are based around. They are usually 1/2 Pokemon that work together well in a deck that really keep it flowing.
For example, In Reshiboar, the cores would be Reshiram and (ability) Emboar.
In Klingklang/Coballion it's, well, Klingklang and Coballion. Darkrai or Mewtwo decks consist of Darkrai EX and Mewtwo EX. Eels are Eelektross.ETC

So yeah, pretty close to the video game. You build a deck around a strategy, and the Pokemon that carry out that strategy, and then construct the deck to better that strategy and make it flow correctly.